# Properties

 Label 139650gd Number of curves $4$ Conductor $139650$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("139650.cr1")

sage: E.isogeny_class()

## Elliptic curves in class 139650gd

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
139650.cr4 139650gd1 [1, 0, 1, -12276, -894302] [2] 663552 $$\Gamma_0(N)$$-optimal
139650.cr3 139650gd2 [1, 0, 1, -232776, -43230302] [2, 2] 1327104
139650.cr2 139650gd3 [1, 0, 1, -269526, -28677302] [2] 2654208
139650.cr1 139650gd4 [1, 0, 1, -3724026, -2766405302] [2] 2654208

## Rank

sage: E.rank()

The elliptic curves in class 139650gd have rank $$0$$.

## Modular form 139650.2.a.cr

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} + q^{4} - q^{6} - q^{8} + q^{9} - 4q^{11} + q^{12} - 2q^{13} + q^{16} - 2q^{17} - q^{18} + q^{19} + O(q^{20})$$

## Isogeny matrix

sage: E.isogeny_class().matrix()

The $$i,j$$ entry is the smallest degree of a cyclic isogeny between the $$i$$-th and $$j$$-th curve in the isogeny class, in the Cremona numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with Cremona labels.